Question: Solve for $x$ and $y$ using elimination. ${-6x+2y = -34}$ ${-5x+y = -31}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-2$ ${-6x+2y = -34}$ $10x-2y = 62$ Add the top and bottom equations together. $4x = 28$ $\dfrac{4x}{{4}} = \dfrac{28}{{4}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-6x+2y = -34}\thinspace$ to find $y$ ${-6}{(7)}{ + 2y = -34}$ $-42+2y = -34$ $-42{+42} + 2y = -34{+42}$ $2y = 8$ $\dfrac{2y}{{2}} = \dfrac{8}{{2}}$ ${y = 4}$ You can also plug ${x = 7}$ into $\thinspace {-5x+y = -31}\thinspace$ and get the same answer for $y$ : ${-5}{(7)}{ + y = -31}$ ${y = 4}$